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Block #97,697

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/4/2013, 8:47:55 PM Β· Difficulty 9.3153 Β· 6,729,035 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
7e4d49a8eb53e0d0e921e0a5817539328feb7cff50e1c37a5e76c25383ffe0f2
View on Chainz β†—

Height

#97,697

Difficulty

9.315299

Transactions

1

Size

200 B

Version

2

Bits

0950b76c

Nonce

43,516

Timestamp

8/4/2013, 8:47:55 PM

Confirmations

6,729,035

Mined by

⛏️ P2SHAGNF5FM1iDMi8svUwibLBo1iJFn54CJy51

Merkle Root

ed155b1d368df9b7cd7605dad46b3a028f0d843f32564fb9e4c0ebbb61c82801
Transactions (1)
Coinbaseed155b1d368df9…c0ebbb61c82801
1 in β†’ 1 out11.5100 XPM109 B
AGNF5FM1…n54CJy51
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.594 Γ— 10⁹⁢(97-digit number)
25949580629953560845…63087394278255622079
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin βˆ’ 1
2.594 Γ— 10⁹⁢(97-digit number)
25949580629953560845…63087394278255622079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.189 Γ— 10⁹⁢(97-digit number)
51899161259907121690…26174788556511244159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.037 Γ— 10⁹⁷(98-digit number)
10379832251981424338…52349577113022488319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.075 Γ— 10⁹⁷(98-digit number)
20759664503962848676…04699154226044976639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.151 Γ— 10⁹⁷(98-digit number)
41519329007925697352…09398308452089953279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.303 Γ— 10⁹⁷(98-digit number)
83038658015851394704…18796616904179906559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.660 Γ— 10⁹⁸(99-digit number)
16607731603170278940…37593233808359813119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.321 Γ— 10⁹⁸(99-digit number)
33215463206340557881…75186467616719626239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.643 Γ— 10⁹⁸(99-digit number)
66430926412681115763…50372935233439252479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,858,010 XPMΒ·at block #6,826,731 Β· updates every 60s
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